Algebraic properties of the maps $\chi_n$

ePrint Report: Algebraic properties of the maps $\chi_n$

Jan Schoone, Joan Daemen

The Boolean map $\chi_n \colon \mathbb{F}_2^n \to \mathbb{F}_2^n,\ x \mapsto y$ defined by $y_i = x_i + (x_{i+1}+1)x_{i+2}$ (where $i\in \mathbb{Z}/n\mathbb{Z}$) is used in various permutations that are part of cryptographic schemes, e.g., Keccak-f (the SHA-3-permutation), ASCON (the winner of the NIST Lightweight competition), Xoodoo, Rasta and Subterranean (2.0).
In this paper, we study various algebraic properties of this map.
We consider $\chi_n$ (through vectorial isomorphism) as a …

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